Degenerate complex Monge-Ampere equations on compact Kahler manifolds have been recently intensively studied using tools from Pluripotential theory. It turns out that this provides a dierent approach to the weak version of the famous Calabi conjecture and allows to extend Calabi-Yau and Aubin-Yau theorems on the existence of Kahler-Einstein metrics to the case of projective varieties with mild singularities. I will survey some recent results obtained with P. Eyssidieux and V. Guedj by emphasizing the r^ole of Pluripotential theory in this approach.